Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/118

104 It is clear, then, that we are entitled to refer the study of sums of series to Pythagoras himself; but whether he went beyond the oblong, and studied pyramidal or cubic numbers, we cannot say.

49. It is easy to see how this way of representing numbers would suggest problems of a geometrical nature. The dots which stand for the pebbles are regularly called "boundary-stones" (ὅροι, termini, "terms"), and the area they mark out is the "field " (χώρα). This is evidently an early way of speaking, and may be referred to Pythagoras himself. Now it must have struck him that "fields" could be compared as well as numbers, and it is likely that he knew the rough methods of doing this traditional in Egypt, though certainly these would fail to satisfy him. Once more the tradition is helpful in suggesting the direction his thoughts must have taken. He knew, of course, the use of the triangle 3, 4, 5 in constructing right angles. We have seen (p. 20) that it was familiar in the East from a very early date, and that Thales introduced it to the Hellenes, if they did not know it already. In later writers it is actually called the "Pythagorean triangle." Now the Pythagorean proposition par excellence is just that, in a right-angled triangle,